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Abstract
In this paper, we study the influence of the inertial effect on frequency synchronization in an ensemble of Kuramoto oscillators with finite inertia and symmetric and connected interactions. We present sufficient conditions in terms of coupling strength, algebraic connectivity, natural frequencies, and the inertial term to guarantee the occurrence of frequency synchronization. We also make a comparison with the existing conditions proposed for the first-order Kuramoto model and conclude that the inertial effect, if appropriately small, has little influence on frequency synchronization as long as the initial phase configurations are distributed in a half circle.
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